The key idea of the linear approximation technique is to give constrains \(l(x)\le f(x)\le u(x),x\in [l,u]\)  of every layer's function \(f(x)\) , including non-linear, fully-connected and convolutional layers. Through propagation, the linear constraints must ensure the value of output will not exceed the upper and lower bounds, which is the key to keeping the soundness of the linear approximation technique. In our work, we fully exploit the CNNs with Maxpool and Sigmoid/Tanh/Arctan functions to give the Tightest linear constraints and make use of the general framework in CNN-Cert [1]}
